Results - Studying the ICM velocity structure within galaxy clusters with simulations and X-ray

complex around 6.7 keV (rest–frame energy), and fit with an absorbedBAPEC⁵ model (see Fig. 5.1 for an example with one of the presented haloes), a velocity– and thermally–

broadened emission spectrum for collisionally–ionised diffuse gas. The model assumes the distribution of the gas non–thermal velocity along the l.o.s. to be Gaussian and the velocity broadening is quantified by the standard deviation, σ, of this distribution.

provide estimates for an EM–weighted–like velocity dispersion. We therefore investigate the relation between mass–weighted and EM–weighted velocity dispersion, σ500,m and σ_500,EM respectively.

The comparison is shown in Fig. 5.3, wherein both values of σ_500,w are calculated for the gas residing within R500, in the plane perpendicular to the l.o.s.. The relation found between the two definitions ofσ500,w is not coincident with the one–to–one relation (overplotted in red in the figure), as the EM–weighted value is likely to be affected by the thermo–dynamical status of the gas⁷, that is by processes such as turbulence, merging and substructures. Despite this, the difference is quite small and the two values are fairly well correlated.

For the purpose of our following analysis and the comparison against synthetic X–ray data, however, we decide to use the EM–weighted velocity dispersion, σ_500,EM, which is more directly related to the X–ray emission of the gas, because of the proportionality between the normalization of the X–ray spectrum and the gas EM itself.

In order to probe the global, dynamical structure of the ICM we would need to observationally measure the gas velocity dispersion within the wholeR500region. However, simulating observations for a telescope like ATHENA we would be able to infer information only about a smaller, inner region. Therefore, we explore the relation between the estimated value of the velocity broadening along the line of sight in different regions of the cluster, shown in Fig. 5.4. It is evident from the figure that the value calculated for the gas within R500 correlates linearly with the value computed in smaller, internal regions, namely for r < 0.3R₅₀₀ (upper panel) and for the region covered by the FoV of ATHENA, ∼0.15R500 (lower panel).

With respect to the one–to–one correlation (red line in Fig. 5.4), however, outliers are present in this sample, showing that prominent substructures in the velocity field of the gas must be present in these clusters. Therefore, the level of complexity in the spatial structure of the ICM velocity field can be singled out by such comparison between the velocity dispersion calculated in the R500 region and the values corresponding to smaller, inner regions.

Nevertheless, the relations discussed ensure that we can safely:

7We recall here that EM =R

nenHdV.

10¹⁵ M₅₀₀ [h^-1 M_sun] 0

200 400 600 800 1000

σ500, m [km/s]

Figure 5.2: Theoretical value of the mass–weighted velocity dispersion, σm, calculated within R500 (in the plane perpendicular to the l.o.s. direction), reported as function of the halo massM500, inh⁻¹M⊙.

0 200 400 600 800 1000 σ500, m [km/s]

0 200 400 600 800 1000

σ500, EM [km/s]

Figure 5.3: Theoretical value of the EM–weighted velocity dispersion,σ500,EM versus the mass–weighted value,σ500,m, in km/s. Both values are calculated for the region withinR500, in the plane perpendicular to the l.o.s. direction. Overplotted in red is the curve referring to the one–to–one relation.

0 200 400 600 800 1000 σ0.3*R500, EM [km/s]

0 200 400 600 800 1000

σ500, EM [km/s]

0 200 400 600 800 1000 σXMS-FoV, EM [km/s]

0 200 400 600 800 1000

σ500, EM [km/s]

Figure 5.4: Relation between the EM–weighted velocity dispersion, σ500,EM, within R500 and the analogous values calculated for: (top panel) the region within 0.3R500 and (bottom panel) the region covered by the FoV of ATHENA, (i.e. ∼ 0.15R500). Overplotted in red is the curve referring to the one–to–one relation.

(i) assume the EM–weighted velocity dispersion instead of the mass–weighted value to trace the intrinsic velocity structure;

(ii) focus on the expected value for the wholeR₅₀₀ region of the cluster, even though the velocity dispersion detectable with ATHENA probes a smaller, inner region, given by the XMS FoV.

5.4.2 Comparison against synthetic data

The ICM velocity dispersion calculated directly from the simulation can here be used to compare against the mock ATHENA data, from which we can use the high–resolution spectroscopy to measure the velocity dispersion of the gas along the line of sight.

Fig. 5.5 shows the comparison between expectations provided by the simulated data (black diamonds) and results from analysis of the synthetic ATHENA spectra (blue asterisks).

The expected velocity dispersion of the gas particles residing in the region corresponding to the ATHENA FoV is calculated according to Eq. 5.1, weighted by

0 10 20 30 40

halo id 0

200 400 600 800 1000 1200

σv [km/s]

sim (kT > 2keV) mock (Fe_line)

Figure 5.5: Comparison between the theoretical expectation of the velocity dispersion σv, calculated directly from the simulation (black diamonds and shaded areas), and the value obtained from the spectral fitting of the synthetic XMS spectra obtained with PHOX (blue asterisks with error bars). The id numbers of the 43 haloes in the sample (x–axis) are ordered according to the increasing halo mass,M500.

the EM, while the values derived from the X–ray spectra are obtained as described in Section 5.3.3, with error bars corresponding to the 1σ errors to the best–fit values. As shown in the Figure, we find very good agreement between simulation (intrinsic, “true”

solution) and synthetic spectral data (observational detections), namely for ∼ 74% of the haloes the spectral analysis of the iron lines provides a measure of the gas velocity dispersion, along the l.o.s., within 20% from the expected value (purple, shaded area). We find, in particular, that∼50% of the halos show agreement at a level better than ∼10%

(internal, pink shaded area in Fig. 5.5). We remark here that the reference number, or halo id in the Figure, is associated to the haloes of the sample in an increasing order for increasing M500.

The deviation between expected and measured velocity dispersion, referring to the XMS FoV as in Fig. 5.5, has been quantified as

δ= σ^mock_v −σ_v^sim

σ_v^sim , (5.2)

and its distribution for the sample is reported in Fig. 5.6.

Clearly, the distribution of δ is peaked around the zero value, reflecting the very good

-1.0 -0.5 0.0 0.5 1.0

deviation 0

5 10 15

# of haloes

deviation = (σv mock-σv

sim)/σv sim

Figure 5.6: Deviation of the best-fitσv from the expected value for all the 43 haloes in the sample.

agreement previously discussed. However, we also find outliers in the sample that show deviations up to ∼43%.

Extreme cases in the sample

Given the distribution of the deviations, reported in Fig. 5.6, we here focus onto two sets of haloes in the sample for which the deviation between simulation and mock data is very minor and most prominent, respectively.

The EM distribution as function of the l.o.s. velocity, for the gas particles in the ATHENA FoV, is shown for the two sets of haloes in Fig. 5.7. The black histograms refer to all the gas in the region, while the overplotted red histograms only account for the hot–phase gas, i.e. particles for which kT > 2 keV. The reason for selecting the hot gas is that it mostly contributes to the iron line emission, from which the velocity broadening is measured.

It is clear from the left–hand–side column in the Figure, corresponding to the most–

deviating haloes, that there are substantial substructures within the gas velocity field.

The red histograms for the haloes that show best agreement (right–hand–side column), instead, reflect more regular distributions of the EM as function of the vl.o.s., indicating more regular velocity fields.

The value estimated from the broadening of the spectral lines is assumed to be the dispersion of the Gaussian distribution that best fits the line shape. Therefore, a more detailed comparison should involve the dispersion of the Gaussian function matching the (red) distribution shown, instead of the theoretical value calculated as in Eq. 5.1. The green curves in Fig. 5.7 define the Gaussian fits to the red distributions, whose σ_v^gauss is more directly comparable to the spectral results.

As an additional comparison, we also overplot the Gaussian curve (blue asterisks) constructed from the theoretical estimation of the EM–weighted values for gas velocity dispersion (Eq. 5.1) and mean l.o.s. velocity. In the most–deviating clusters, the evident differences among the different curves substantially reflects the deviations explored above (see, e.g., the halo with the largest deviation, top–left panel in Fig. 5.7). In particular, the green, best–fit Gaussian clearly fails to capture all the features of the multi–component velocity distribution, which is most likely what happens during the spectral fit. The low level of deviation found for the “best” haloes set (right–hand–side column) is indeed

5 MOST–DEVIATING HALOES 5 LEAST–DEVIATING HALOES

-3000 -2000 -1000 0 1000 2000

vl.o.s. [km/s]

0 2•10⁵ 4•10⁵ 6•10⁵ 8•10⁵

EM/1e60